How Many Pokémon Can You Get with Only Pokémon Red?
Assuming you do not use any glitches, the answer is 124. The Professor Oak challenge guide for Red can be found here, although I've made a shorter list of encounters below in case anything happens to the external guide.
The list of Pokémon you cannot get without trading, which equals 27 species, is as follows:
- Two Starters (6) - 6 total
- As you can only select one starter Pokémon, the other two starters, and their evolutions, are unavailable; this totals 6 Pokémon.
- Trade Evolutions (4) - 10 total
- Golem, Machamp, Alakazam, and Gengar evolve by trade. Without the ability to trade, they are unobtainable.
- Two Eeveelutions (2) - 12 total
- As you only receive one Eevee, you can only receive one of its evolutions.
- One Fossil (2) - 14 total
- As you can only obtain one Fossil in Mt. Moon, you miss out on the other Fossil Pokémon and its evolution.
- One Hitmon (1) - 15 total
- As you can only obtain one Hitmon, you miss out on the other.
- Version Exclusives (11) - 26 total
- The following Pokémon, and their evolutions, cannot be obtained without the use of glitches or trading: Sandshrew, Vulpix, Meowth, Bellsprout, Magmar, Pinsir.
- Mythical/Event (1) - 27 total
- Outside of glitches, Mew was only obtainable via events that are no longer active. However, Mew was never needed to get the certificate from the Game Freak employee.
Professor Oak Challenge Notes
Pre-Badge 1 (Brock)
- Pallet Town: One starter & Evolutions (3 total)
- Route 1: Pidgey, Pidgeotto, Pidgeot (6 total)
- Route 1: Rattata, Raticate (8 total)
- Route 22: Nidoran♂, Nidorino (10 total)
- Route 22: Nidoran♀, Nidorina (12 total)
- Route 22: Spearow, Fearow (14 total)
- Viridian Forest: Caterpie, Metapod, Butterfree (17 total)
- Viridian Forest: Weedle, Kakuna, Beedrill (20 total)
- Viridian Forest: Pikachu (21 total)
Badge 1 through Badge 2 (Misty)
- Route 3: Jigglypuff (22 total)
- Route 4: Magikarp, Gyarados (24 total)
- Mt. Moon: Zubat, Golbat (26 total)
- Mt. Moon: Geodude, Graveler (28 total)
- Mt. Moon: Paras, Parasect (30 total)
- Mt. Moon: Clefairy (31 total)
- Route 4: Ekans, Arbok (33 total)
- Route 24: Abra, Kadabra (35 total)
- Route 24: Oddish, Gloom (37 total)
- Route 5: Mankey, Primeape (39 total)
- Vermilion City: Farfetch'd: Trade Your Spearow (40 total)
- Route 11: Drowzee, Hypno (42 total)
- Diglett's Cave: Diglett, Dugtrio (44 total)
- Route 2: Mr. Mime: Trade Your Abra (45 total)
- Evolve Two Moon Stone Pokémon with Moon Stones from Mt. Moon (47 total)
Badge 2 through Badge 3 (Koga)
- Route 10: Voltorb, Electrode (49 total)
- Rock Tunnel: Machop, Machoke (51 total)
- Rock Tunnel: Onix (52 total)
- Route 8: Growlithe (53 total)
- Celadon City: Eevee & 1 Evolution (55 total)
- Celadon City: Porygon (56 total)
- Buy a Thunderstone: Evolve Pikachu (57 total)
- Buy a Fire Stone: Evolve Growlithe (58 total)
- Buy a Leaf Stone: Evolve Gloom (59 total)
- Evolve Two Moon Stone Pokémon with Moon Stones from Rocket Hideout and Route 2 (61 total)
- Route 16: Doduo, Dodrio (63 total)
- Pokémon Tower: Gastly, Haunter (65 total)
- Pokémon Tower: Cubone, Marowak (67 total)
- Route 16/12: Snorlax (68 total)
- Super Rod in Vermilion City: Shellder, Cloyster (70 total)
- Good Rod in Vermilion City: Poliwag, Poliwhirl, Poliwrath (73 total)
- Good Rod in Vermilion City: Goldeen, Seaking (75 total)
- Super Rod in Vermilion City: Krabby, Kingler (77 total)
- Super Rod on Route 19: Horsea, Seadra (79 total)
- Super Rod on Route 19: Staryu, Starmie (81 total)
- Super Rod on Route 24: Psyduck, Golduck (83 total)
- Super Rod on Route 10: Slowpoke, Slowbro (85 total)
- Super Rod in Viridian City: Tentacool, Tentacruel (87 total)
- Cerulean City: Jynx: Trade Your Poliwhirl (88 total)
- Route 18: Lickitung: Trade Your Slowbro (89 total)
- Route 14: Ditto (90 total)
- Route 14: Venonat, Venomoth (92 total)
- Super Rod in Safari Zone: Dratini, Dragonair, Dragonite (95 total) (alternatively, purchase a Dratini at Celadon Game Corner)
- Safari Zone: Exeggcute, Exeggutor (97 total)
- Safari Zone: Rhyhorn, Rhydon (99 total)
- Safari Zone: Chansey (100 total)
- Safari Zone: Scyther (101 total) (alternatively, purchase a Scyther at Celadon Game Corner
- Safari Zone: Tauros (102 total)
- Safari Zone: Kangaskhan (103 total)
- Saffron City: One Hitmon (104 total)
- Silph Co.: Lapras (105 total)
Badge 3 through Badge 4 (Erika)
- Power Plant: Magnemite, Magneton (107 total)
- Power Plant: Electabuzz (108 total)
- Power Plant: Zapdos (109 total)
- Route 21: Tangela (110 total) (alternatively, trade your Venonat at Cinnabar Lab)
- Cinnabar Lab: Aerodactyl (111 total)
- Cinnabar Lab: Fossil & Evolution (113 total)
- Pokémon Mansion: Koffing, Weezing (115 total)
- Pokémon Mansion: Grimer, Muk (117 total)
- Pokémon Mansion: Ponyta, Rapidash (119 total)
- Seafoam Islands: Seel, Dewgong (121 total) (alternatively, trade your Ponyta at Cinnabar Lab)
Badges 4 through 8
- Seafoam Islands: Articuno (122 total)
Badge 8 through Elite Four
- Victory Road: Moltres (123 total)
Post-Elite Four
- Cerulean Cave: Mewtwo (124 total)